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Dynamic analysis of a harvested fractional-order biological system with its discretization

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  • Al-Nassir, Sadiq

Abstract

The complexity of nature that can not be modeled by means of ordinary or partial differential equations. This paper aims to study the dynamics behavior of fractional-order prey-predator system and its discretization with harvesting on prey species. The logistic growth of prey species and Holling type III functional response are considered. The existence and the local stability of all equilibria of fractional-order system, as well as its discretization, are determined and investigated. Then the discrete model is extended to an optimal control problem to get an optimal harvesting policy. We use the discrete version of Pontryagin maximum principle to derive the characterization of the optimal harvesting control and the optimal corresponding state solution. Numerical simulations are given to illustrate the theoretical findings.

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  • Al-Nassir, Sadiq, 2021. "Dynamic analysis of a harvested fractional-order biological system with its discretization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006627
    DOI: 10.1016/j.chaos.2021.111308
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    1. Ortigueira, Manuel & Bengochea, Gabriel, 2017. "A new look at the fractionalization of the logistic equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 554-561.
    2. Hoekstra, Jeljer & van den Bergh, Jeroen C.J.M., 2005. "Harvesting and conservation in a predator-prey system," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1097-1120, June.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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    Cited by:

    1. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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